By Piet Van Mieghem
Publisher: Cambridge University Press
Print Publication Year: 2006
Online Publication Date:February 2010
Online ISBN:9780511616488
Hardback ISBN:9780521855150
Paperback ISBN:9780521108737
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511616488.014
Subjects: Communications and signal processing, Statistics for physical sciences and engineering
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Queueing theory describes basic phenomena such as the waiting time, the throughput, the losses, the number of queueing items, etc. in queueing systems. Following Kleinrock (1975), any system in which arrivals place demands upon a finite-capacity resource can be broadly termed a queueing system.
Queuing theory is a relatively new branch of applied mathematics that is generally considered to have been initiated by A. K. Erlang in 1918 with his paper on the design of automatic telephone exchanges, in which the famous Erlang blocking probability, the Erlang B-formula (14.17), was derived (Brockmeyer et al., 1948, p. 139). It was only after the Second World War, however, that queueing theory was boosted mainly by the introduction of computers and the digitalization of the telecommunications infrastructure. For engineers, the two volumes by Kleinrock (1975, 1976) are perhaps the most well-known, while in applied mathematics, apart from the penetrating influence of Feller (1970, 1971), the Single Server Queue of Cohen (1969) is regarded as a landmark. Since Cohen's book, which incorporates most of the important work before 1969, a wealth of books and excellent papers have appeared, an evolution that is still continuing today.
A queueing system
Examples of queueing abound in daily life: queueing situations at a ticket window in the railway station or post office, at the cash points in the supermarket, the waiting room at the airport, train or hospital, etc. In telecommunications, the packets arriving at the input port of a router or switch are buffered in the output queue before transmission to the next hop towards the destination.
pp. i-iv
pp. v-x
pp. xi-xii
pp. 1-6
Part I - Probability theory: Read PDF
pp. 7-8
2 - Random variables: Read PDF
pp. 9-36
3 - Basic distributions: Read PDF
pp. 37-60
pp. 61-82
pp. 83-96
pp. 97-112
Part II - Stochastic processes: Read PDF
pp. 113-114
7 - The Poisson process: Read PDF
pp. 115-136
pp. 137-156
9 - Discrete-time Markov chains: Read PDF
pp. 157-178
10 - Continuous-time Markov chains: Read PDF
pp. 179-200
11 - Applications of Markov chains: Read PDF
pp. 201-228
12 - Branching processes: Read PDF
pp. 229-246
13 - General queueing theory: Read PDF
pp. 247-270
14 - Queueing models: Read PDF
pp. 271-316
Part III - Physics of networks: Read PDF
pp. 317-318
15 - General characteristics of graphs: Read PDF
pp. 319-346
16 - The Shortest Path Problem: Read PDF
pp. 347-386
17 - The effciency of multicast: Read PDF
pp. 387-416
18 - The hopcount to an anycast group: Read PDF
pp. 417-434
Appendix A - Stochastic matrices: Read PDF
pp. 435-470
Appendix B - Algebraic graph theory: Read PDF
pp. 471-492
Appendix C - Solutions of problems: Read PDF
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